where \(h_\lambda \)  is the homogeneous symmetric function associated with \(\lambda \) , \(e_n\) 
the \(n\) -th elementary symmetric function, and \(\nabla \)  the Garsia-Haiman nabla operator acting on symmetric functions. 

It is clear that \(_n\)  is bigraded by \(x,y\) -degree and that this decomposition respects the \(W\) -action. The \(q,t\) -Frobenius character is given by Haiman [1]} as the symmetric function \(\nabla e_n\)  where \(\nabla \)  is the Garsia-Haiman \(\nabla \) -operator on symmetric functions and \(e_n\)  is the \(n\) -th elementary symmetric function.
